Photon absorption process

Post number 11, the one by Zoobyshoe explaining what Claude meant by the rope analogy using a billiard ball analogy, arises 2 questions:

1) Please explain how this works, the process through which the photon 'perturbs' the electric field without exciting the atom

2) Once the Medium is 'perturbed' and sticking to the billiard analogy, it reaches the last ball, how does it then Release the momentum of the atom that doesn't have an excited electron, and become a wave again

Of course, that must be only for if it stops becoming a wave once it perturbs the electric field. But if it does not stop being a wave while the field is perturbed, then i must misunderstand the analogy, or am missing something. Then if it maintains being a wave, even while the atom is perturbed, then how does the wave slow down? So therefore I surmise it must not be a wave during the "perturbation."

The very first line of my post may be misconstrued to seem irritatingly simple. (Don't judge!)

Well, it's not. What I meant on the very first line I wrote, was quite deep, at least for my knowledge, I know a photon of a correct frequency can excite an electron- it absorbs it. How does it absorb it? What is the process through which it does this? How can we know for sure? Is it all just a commonly believed, untestable theory?